Energy Dissipating Devices in Falling Rock Protection Barriersdownload.xuebalib.com/bo1EfhnZcoI.pdf · rock impact and reduce the mechanical stresses in the rest of the elements of

ORIGINAL PAPER

Energy Dissipating Devices in Falling Rock Protection Barriers

L. Castanon-Jano1 • E. Blanco-Fernandez1 • D. Castro-Fresno1 • F. Ballester-Muñoz1

Received: 26 August 2015 / Accepted: 11 November 2016

� Springer-Verlag Wien 2016

Abstract Rockfall is a phenomenon which, when uncon-

trolled, may cause extensive material damage and personal

injury. One of the structures used to avoid accidents caused

by debris flows or rockfalls is flexible barriers. The energy

dissipating devices which absorb the energy generated by

rock impact and reduce the mechanical stresses in the rest

of the elements of the structure are an essential part of

these kinds of structures. This document proposes an

overview of the performance of energy dissipating devices,

as well as of the role that they fulfil in the barrier. Fur-

thermore, a compilation and a description of the dissipating

elements found in the literature are proposed. Additionally,

an analysis has been performed of the aspects taken into

account in the design, such as experimental (quasi-static

and dynamic) tests observing the variation of the behaviour

curve depending on the test speed and numerical simula-

tions by means of several finite element software packages.

Keywords Rockfall flexible barrier � Energy dissipatingdevice � Dynamic behaviour

1 Introduction

Falling rock events can cause dangerous situations, espe-

cially when they occur close to towns, roads, railways or

places with human transit. In such cases, material and

personal damage must be avoided by placing protective

systems. A wide variety of slope protection techniques

exists, which cover different ranges of energy absorption

and are suitable for landslides of different character (Chen

et al. 2013; Descoeudres 1988; Descoeudres et al. 1999;

Volkwein et al. 2011).

Traditionally, the design of rockfall protection systems

was based on the rigidity and resistance of their compo-

nents in order to provide a long useful life. Rigid walls

were used (Peila et al. 2007), covering an absorption of

energy up to 50 kJ (Volkwein and Gerber 2011). Rockfall

galleries (Schellenberg and Vogel 2009) are rigid struc-

tures designed for a high frequency—more than once a

week (López Quijada 2007)—of medium magnitude

events, with a maximum absorbed energy of around

2000 kJ (Volkwein and Gerber 2011). Both rigid walls and

rockfall galleries require large volumes of material or

extensive placement. The problem appears when the rocks

fall from areas which are difficult to reach, or when the

natural conditions do not allow the building of large,

complex structures to prevent damages. The development

of flexible barriers (Fig. 1) addressed this point, covering a

wide range of energy absorption, from 150 kJ (López

Quijada 2007) up to 8000 kJ (Escallón and Wendeler

2013). They consist of a steel mesh surrounded by steel

cables that are connected to steel posts, keeping the mesh

extended. When a rock impacts in the mesh, loads are

transmitted through the cables up to the anchorages on the

ground. First designs had embedded posts and could be

inserted at the top of concrete walls, resulting in low-ca-

pacity protection (de Miranda et al. 2015). Displacement of

some of the barrier components with the rock until it

stopped was enabled, allowing rotation at the base of the

posts, using upslope and lateral cables in order to keep the

barrier in its position. The increase in flexibility results in a

higher load actuation time (known as braking time) and

& L. [email protected]

1 GITECO (Construction Technology Applied Research

Group), Civil Engineering School, University of Cantabria,

Santander, Spain

123

Rock Mech Rock Eng

DOI 10.1007/s00603-016-1130-x

http://crossmark.crossref.org/dialog/?doi=10.1007/s00603-016-1130-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1007/s00603-016-1130-x&domain=pdf

hence a reduction in the maximum load on all the com-

ponents of the structure. Energy dissipaters are an essential

device in this context, due to the increase in the energy

absorption capacity with respect to non-braking barriers.

The maximum absorbed energy of a barrier without brakes

is 100 kJ (Muraishi et al. 2005). The adding of brakes to

the rockfall protection systems allowed the development of

high energy absorption barriers with a maximum value of

8500 kJ (Maccaferri) nowadays.

Energy dissipating devices may be defined as the

mechanisms incorporated into the flexible barrier system to

absorb internal energy, helping to reduce stresses within

the structure in a rock impact. These devices transform the

kinetic and potential energy of the falling materials into

deformation energy, fracture or heat generated by friction.

These elements can also be called brake devices, brake

elements or brakes.

Some predecessors of the current energy dissipater were

designed to make the barrier more flexible. These devices

elastically deform while tension exists, recovering their

shape when it ends (López Quijada 2007). They are

wrongly called energy dissipaters because they do not

contribute to dissipation, but absorb the energy within the

elastic range of deformation. The energy is recovered by

the system when the components retake their original

shape. This solution involves a reduction in the stresses in

the cables where the device is connected until the end of its

stroke. Then, the cable begins to load according to its real

(and stiffer) load–displacement curve. Figure 2 shows a

device based on the compression of its neoprene compo-

nents. Post-bases are another option to place this type of

devices (Fig. 2b). The anchoring of the posts is freed by the

addition of the device. A small degree of rotation is

allowed in the perpendicular plane of the barrier, recov-

erable a posteriori.

It is considered that in 1975 the first ‘‘real’’ brake ele-

ment was designed and installed in a dynamic barrier by

Brugg Cable Products (Smith and Duffy 1990). Since then,

numerous devices have been invented to improve the bar-

rier behaviour. In total, 174 patent families (inventions)

have been found describing a new energy dissipating

device or a new barrier in which these devices play an

important role. The 174 patent families represent 120 dif-

ferent assignees, Fatzer (a company of the Brugg group)

and Pfeifer Isofer being the most significant in both num-

bers of applications and granted IPR (intellectual property

rights) (Verbeke 2015). The most representative brake

devices will be described in this paper. The selection of the

brakes will be based on knowledge of their behaviour and

specific data about energy absorption.

Nowadays, the design and evaluation of new brakes can

be accomplished with the help of two different procedures.

The first, based on experimental tests, gives essential

information about the behaviour curve of the prototype.

The most recent tests are dynamic in order to make the

brake work in a similar way to real conditions. This paper

provides an overview of all experimental test types per-

formed on brakes and presents a comparative analysis of

the available data about brakes, comprising activation

force, mean running force and dissipated energy. The

second tool to help in brake design is numerical simulation.

Geometrical optimization can be carried out with this

technique, as well as an analysis of the effect of the brakes’

position on the complete barrier behaviour. A compilation

of all the approaches enables us to see the great potential of

computational tools.

2 Description of the Existing Brakes

Brake elements currently on the market are grouped in 4

classes according to the way they dissipate energy:

• Brake elements by pure friction.• Brake elements by partial failure.• Brake elements by plastic deformation.• Brake elements by mixed friction/plastic deformation.

2.1 Brake Elements by Pure Friction

They were the first brakes to be invented due to their

simplicity, mainly using the support cables of the barrier

and friction clamps connected to a plane surface. Pressure

is applied on the clamp by the bolts’ torque.

The brake in Fig. 3a (Smith and Duffy 1990) consists

of a looped cable. The cross of the cable is pressed by a

Fig. 1 Flexible barrier components. The interception structurereceives the impact of the rock. It is usually made of cable or ring

nets and a secondary layer of a wire mesh with finer gap size to

collect smaller rocks. Loads are transmitted through the perimeter,

upslope and lateral cables to the ground

L. Castanon-Jano et al.

123

friction clamp with four bolts. The EI brake (Smith and

Duffy 1990) in Fig. 3b comprises a clamp where two

cables go through. Two ends of the cables are connected

to the lateral or upslope anchor and to the free end of the

post. The other ends of the two cables are free to allow

the friction process up to a limited length. The brake in

Fig. 3c (Trad et al. 2013) consists of the compression of

a cable on a plate through a clamp with two bolts. This

cable is fixed at one end to the post, and the other end is

free to allow slippage in the clamp. In order to ensure

the transmission of force to the ground, the plate is

connected to another cable that is fixed to an anchor.

The brake in Fig. 3d uses the same dissipation mecha-

nism as the previous one, substituting the fixed con-

nection of the cable in the plate by another clamp ? bolt

system (Peila et al. 1998). In this way, both the cables

coming from the post and the anchor are able to slide

dissipating energy.

Fig. 2 Elastic devices a in lateral cables, reducing stresses in the connecting components, and b in a post-base, allowing a small rotation andreducing the stiffness of the barrier

Fig. 3 Friction brakes: a loop brake (Brugg AG), b two plates compression (EI Enterprise Industrielle), c simple friction brake (G.T.S.) andd double friction brake (E.L.I.T.E TUBOSIDER)

Energy Dissipating Devices in Falling Rock Protection Barriers

123

A disadvantage of this kind of brakes is the use of the

support and connection cables in the braking mechanism,

which could bring on local failures. Furthermore, the

inaccuracy of the bolts’ torque can lead to obstruction of

the cables or a poor friction dissipation process.

2.2 Brake Elements by Plastic Deformation

The energy absorption of this kind of brakes is based on the

non-recoverable deformation of some of their components.

A simple system is shown in Fig. 4 (Von Allmen 2004).

It includes a metal spiral connected at its ends to the cables

by shackles. When tension is created in the cables, the

spiral stretches deforming plastically.

2.3 Brake Elements by Partial Failure

This type of brake elements is the least common. The first,

illustrated in Fig. 5a, is comprised of a tube within which

two cables move in opposite directions from each side

(López Quijada 2007). These drag a sharpened piece,

which when entering in the tube divides it and dissipates

energy. The work performed by the forces in the brake

element to absorb kinetic energy is the same as the cut

resistance of the tube multiplied by the cut length. The

disadvantage with the system is that great opposition to the

cut may trigger cable rupture or tube deformation by

buckling. On the other hand, low opposition to the cut

could cause a quick working of the brake and the energy

dissipation would be lower than expected. The second

brake shown (Fig. 5b) consists of a series of cables con-

nected in parallel, each one longer than the previous one

(Thomel 1998). The working sequence is as follows: the

shortest cable is the only one bearing the loads induced by

the rockfall. When the ultimate strength is overcome, the

cable breaks and the load is transmitted to the cable

immediately following in length, which will in turn break

when, once again, the load becomes greater than can be

tolerated by the cable. This cycle goes on while the load

can be supported by one of the cables.

The brake in Fig. 5c is composed of a stack of steel

rings. The cable is folded, introduced through one end of

the stack and attached at the opposite end around a pivot.

The cable’s traction leads to compression and plastic

deformation of each of the metal rings and then to their

breaking sequentially (Moreillon 2006). The load tolerated

by the brake will depend on the metal rings’ size, and the

maximum elongation will be proportional to the number of

rings placed together forming the casing. The most recent

dissipater in this group is shown in Fig. 5d (Fulde and

Müller 2013). It comprises a disc with a series of drilled

holes in a spiral pattern. When the cables transmit the force

to the brake, the material between the holes deforms

plastically, one after another, until failure. At the same

time, the two arms generated by these breaks tighten

obtaining a single strip when the dissipater is fully

elongated.

Brake elements by partial failure can be dangerous due

to the possibility of rupture in unexpected zones of the

brake (Fulde and Müller 2013). The preservation of brake

integrity is essential. Otherwise the connections of the free

end of posts with the anchors would fail leaving the barrier

inoperable. Metal disc brakes (Fig. 7c) are installed in a

continuous cable where there are no discontinuities;

therefore, when all the discs break, the cable bears the

loads preserving the barrier integrity. If continuity of the

cable is not possible, a good solution is to add a parallel

cable attached to both ends of the brake, as has been done

in the Pfeifer brake (Fig. 7d). The cable in parallel included

in the Pfeifer brake has the same or higher resistance to the

cable in which the brake is installed and the same length as

the maximum elongation the brake can stand. In this way,

if the brake collapses, the auxiliary cable will preserve the

brake element integrity.

2.4 Mixed Brake Elements: Friction/Deformation

The first brake element with these characteristics was

created by the Tubosider company (Peila et al. 1998). It is

composed of a metal tube through which cables pass from

both ends via a plug in each end (Fig. 6a). When the load is

transmitted to the brake, the cables move in opposite

directions taking the plugs with them. The energy

absorption occurs both by the plugs’ friction and by the

tube’s buckling. A disadvantage of this type of brake is the

possibility of blocking of the plugs and reduction in the

expected absorbed energy.

The next brake element that used both dissipation

mechanisms was designed by Fatzer AG and used by

Geobrugg (Fig. 6b). In this device, the cable is conducted

through a protective pipe in a ring shape. An aluminiumFig. 4 Spiral brake element by deformation (TRUMER)

L. Castanon-Jano et al.

123

sleeve acts as a compression element and fastens both ends

of the tube. The tension caused by the rockfall on the cable

leads to pipe-sleeve friction and the consequent pipe

deformation (Grassl et al. 2003). Later, Malla Talud Can-

tabria developed a brake that changed the ring pipe for two

U pipes and added another compression sleeve (del Coz

et al. 2010). The two compression sleeves connect the two

U pipes through their ends (Fig. 6c). Tension in the cable

makes the pipes slide in the sleeves and deform plastically

at the same time. The pressure applied on the aluminium

sleeves must be controlled. Otherwise, the same disad-

vantages as mentioned in the friction brakes section would

make these brakes lose part of their dissipation capacity.

The brake in Fig. 6d (Trad et al. 2011) consists of a

square profile with two plugs at the ends. The cable passes

inside the profile several times fastening the plugs in their

position. When load is applied on the cable, it presses and

rubs both plugs inducing the buckling of the profile with

plastic deformation. Thus, the energy dissipation occurs by

friction of the cable with the plugs and the tube and plastic

deformation due to buckling of the tube. In the same way,

the Maccaferri brake (Fig. 6e) is composed of two steel

tubes and two rigid perforated plugs at the ends. Two

cables coming from opposite directions pass through the

tubes and are fixed in the plugs. When a rock impacts on a

flexible barrier, the load transmission makes the plugs press

against the tubes, generating buckling in the tube, with

plastic (hence non-recoverable) deformation. In this brake,

the friction occurs between the tubes and the cables. In

brakes by buckling, especially in those which have square

profiles, cracking could appear at the edge area, since this

is the most affected by the deformation when generating

the folds.

The most recent mixed brakes consist of two steel bars

that bend around a mandrel forming a U shape (Fig. 6f).

When a block impacts on the barrier, the bars displace 1808around the mandrel absorbing energy by friction and

plastic deformation. At the end of the bars, an element is

placed widening the section, avoiding the discontinuity of

the structure if the bars move all the way through the

mandrel (Escallón et al. 2014). A variant of this brake

substitutes the two bars by a metal sheet which performs

the same function. These two brakes are light, making their

installation and substitution easier than others which are

more voluminous.

3 Design

Due to the different geometries and dissipation methods of

the brakes, their design method is not standardized as

happens with other barrier components, like ties (EN

13411-5:2004?A1:2008) or ground anchors (EN 1537).

With the evolution of flexible barriers, several national

and European guidelines were developed (NFP 95 308

1996; Gerber 2001; EOTA 2008; Peila and Ronco 2009)

Fig. 5 Brake elements bypartial failure: a by tube cutting(Sisyphe) b by cables in parallel(Sol Systemes), c metal discs’case (Tecnap Sàrl) and d Pfeiferbrake system (Pfeifer)

Energy Dissipating Devices in Falling Rock Protection Barriers

123

that explain the procedure in full barrier testing and

establish the technical assessment of the fitness for use of

this product. Only the ETAG 027 (EOTA 2008) gives

recommendations for brakes, suggesting the performance

of a quasi-static test in a tensile machine at 2 mm/s speed

and establishing a maximum elongation of 1 m. This value

of elongation is the only design restriction, and it is cor-

rectly fixed to limit the maximum lowering of the barrier.

The absence of standardized methodologies for barrier

design leaves the way open for manufacturers to choose the

number, arrangement and absorption capacity of the

brakes.

There are three suitable places to install the brakes:

lateral wire ropes, upslope wire ropes and perimeter wire

ropes (Fig. 7). In high energy barriers, brakes are placed

in series. This set-up is not certified by the ETAG and

maximum elongation of 1 m must be taken into account.

Brake elements allow a less stiff behaviour in upslope and

lateral wire ropes. Thus, the loading duration in the barrier

caused by a rock impact increases and the peak force is

reduced.

Most manufacturers use barrier prototype testing to

optimize the number, location and energy level of brakes

(Smith and Duffy 1990). If it is considered that some ele-

ment does not dissipate enough energy, or on the contrary,

if it is oversized, it is substituted by another element con-

sidered more suitable for the location in which it is placed.

This is an expensive method, although due to the difficulty

found in the barrier dynamics, it is the most frequently used

one. Therefore, some manufacturers may use numerical

simulations using finite element/finite difference software.

The numerical model, calibrated by means of the experi-

mental data of their components, can be used as a sizing

method, offering illustrative calculations that must be

verified by real tests on the full barrier (Gentilini et al.

2013).

Fig. 6 Mixed brake elements: a tube (Tubosider), b ring (Fatzer AG), c double tube in U (Malla Talud Cantabria), d square profile type (G.T.S.),e double tube type (Maccaferri), f1 bars ? mandrel (Geobrugg) and f2 steel plate ? mandrel (Geobrugg)

L. Castanon-Jano et al.

123

3.1 Design Criteria

When designing a brake, four essential aspects have to be

taken into account:

• Integrity

The brakes must be designed to avoid failure when they

exhaust their available displacement, that is to say avoiding

their separation into 2 parts. This would cause the failure of

the anchorage points in the barrier, leading to instability as

well as inefficacy in the rock retention. In some cases, the

continuity is guaranteed by incorporating the cable itself

into the restraining system where the brake element is fitted

(see ring brake in Fig. 6b). Moreover, intertwined devices

have been designed that avoid their separation (see Malla

Talud Cantabria brake in Fig. 6c). The installation of

protection cables is another solution to prevent collapse

(see Pfeifer brake in Fig. 5d). In this way, if the brake

collapsed, the auxiliary cable would preserve the barrier

integrity. Stops at the end of the cable stroke avoid an

excessive elongation of the brake, working as a displace-

ment limiter.

• Adaptability

Versatile brake elements are required, in which param-

eters such as materials, friction level or friction coefficients

among components, dimensions, etc., can vary, generating

options regarding their absorption capacity. In the case of

brakes that employ a friction mechanism, the two

components of the friction force—the friction coefficient land the normal force N—can be varied in order to adapt the

brake to the needs of the barrier. The friction coefficient

depends on the two materials in contact, and also on the

temperature, roughness of surfaces and relative velocity

between surfaces. Normal force can vary, changing the

pressure between the pieces of the brake in contact. The

mechanical properties of the material also affect the energy

absorption, providing adaptability to the brakes which

work by deformation. Trad (2011) tested brakes in two

different materials: steel and aluminium, and concluded

that the choice would depend on the energy required by the

flexible barrier. Thus, the aluminium brake, with a lower

resistance to buckling, could be used in a low energy

barrier, while steel could be used in high energy barriers.

The variation of any dimension in a component of a brake

makes the force vary and hence so too the absorbed energy.

For example, the greater the thickness of the tubes in the

Maccaferri brake (Fig. 4a), the higher the opposing force to

buckling.

• Durability

Since in most cases brake elements will suffer the

harshness of climate, it is important to consider resistance

to humidity, corrosion and temperature. One solution to

prevent corrosion could be the use of stainless materials or

materials with a protective stainless layer. With respect to

humidity, there are no studies determining the variability of

the behaviour of brakes under rainy conditions. It can be

Fig. 7 Installation of brake elements in a lateral wire ropes, b upslope wire ropes, or c in perimeter wire ropes, d brake elements in series

Energy Dissipating Devices in Falling Rock Protection Barriers

123

assumed that, when the surfaces of the brake are wet, the

friction coefficient decreases and energy dissipation

capacity is lower. Furthermore, the fall of any isolated

boulder or element from the area must be prevented so that

it does not interfere with the brake mechanism negatively

affecting its performance.

• Service Limit State

It will depend on the number of impacts of different

energy, that is, an event on a barrier may make the brakes

work only partially, or even not to work at all, so they

would be able to resist other events without making any

changes in the barrier. Currently, brakes are designed to

have a short useful life in relation to the other barrier

components, since they are designed as the weakest ele-

ment of the structure, and are connected in such a way that

they are easily replaced.

3.2 Experimental Tests

The design of a brake element starts by defining its beha-

viour, by means of the identification of the energy dissi-

pation method. Additionally, characterization of its

performance with a force–displacement graph is necessary

in order to find out the energy absorption capacity. For this,

quasi-static and dynamic tests are performed.

3.2.1 Quasi-Static Test

The quasi-static test consists of fixing one of the cable ends of

the brake to a fixed point and pulling on the other cable end

using a horizontal traction machine (Fig. 8a). The applied

load values are measured by a load cell, and a displacement

sensor checks the relative displacement between each of the

brake ends. Most companies and researchers have performed

quasi-static tests on their brake systems (Smith and Duffy

1990; Peila et al. 1998; Grassl et al. 2003; Castro-Fresno et al.

2009; Bertrand et al. 2012; Fulde andMüller 2013), following

the recommendation of the ETAG027. Load–displacement

curves obtained from the quasi-static tests have the same

pattern (Fig. 9). There is a first section where elastic (recov-

erable) deformation occurs until reaching FA, corresponding

to the activation force of the brake. In section A-B, the

absorption mechanisms work. This section may not be linear,

but can have different shapes: a zigzag, wave, increasing or

irregular form, depending on the technology of the brake. It

tends to have less stiffness than the first branchOA.At the end

of the static test, the system (composed of the brake and the

cable) behaves like a single cable, corresponding to the

hardening branch BC.

A collection of behaviour curves from quasi-static tests

of brakes, numbered from 1 to 9, is presented in Table 1.

For an accurate analysis of brake behaviour, the

assumption of the suitability of quasi-static tests suggested

by the ETAG027 is not enough, the performance of

dynamic tests being advisable. As a demonstration, the full

barrier tests carried out by Peila et al. (1998) resulted in no

activation of some brakes of the barrier, contrary to what

was expected, due to the lack of consideration of the inertia

and the load speed in the deformation of brakes.

(a) (c)

Load cellBrake

Weight: initial position

Displacement measurement

scale

Cable

Weight: final position

CableBrake

Elongated brake

Fixed end attached to the machine Traction point

Cable F

INITIAL STATE

FINAL STATE

Cable

(b)

Final state

Intermediate state

Initial state E=mgh

Free falling massBrake

Fig. 8 Scheme of experimental tests in brakes: a quasi-static test,b free falling block: the brake is fixed at one end to the cliff and at theother end to a block, which is dropped from a specific height, and

c impact test: the brake is placed in a horizontal cable and a weight isdropped vertically

Fig. 9 Typical load–displacement curve from a quasi-static test

L. Castanon-Jano et al.

123

Table 1 Behaviour curves of different brakes extracted from quasi-static tests

=27-182 kN=27-182 kN=-=12.7-38 mm=381 mm=-/δ =26.09-

75.81-103.04 kJ/m

=45 kN=62 kN=-=26 mm=381 mm=-/δ =48.5 kJ/m

=100 kN=110 kN=190 kN=208 mm=2666 mm=3000 mm/δ =100 kJ/m

Smith et al., 1990 Smith et al., 1990 Trad et al., 2013

=65-100 kN=45-68 kN=-=38-108 mm=210 mm=-/ =38.97-

41.56-56.38-62.02

kJ/m

=38 kN=62 kN=95 kN=150mm=1010 mm=1035 mm/δ =24.56 kJ/m

=96.4 kN=140 kN=250 kN=190 mm=2210 mm=2370 mm/δ =100 kJ/m

Peila et al., 1998 Peila et al., 1998 Trad et al., 2011

=75.72 kN=-

=260 kN=26.49 mm

=-=920 mm/

= 59.35 kJ/m

=7-60 kN=20-78 kN=140-160 kN=53-100 mm=180-720 mm=790-870 mm/ =13-53.5-

68.2 kJ/m

=20 kN=30 kN=-

=7.3 mm=850 mm

=-/ =29.16 kJ/m

Grassl et al., 2003 Castro-Fresno et al., 2009 Fulde et al., 2013

1 2 3

4 5 6

7 8 9

Energy Dissipating Devices in Falling Rock Protection Barriers

123

3.2.2 Dynamic Test (Type 1)

The development of dynamic tests arose with the aim of

approximating more to real conditions. This high-speed

system (Bertrand et al. 2012; Trad et al. 2013) consists of

fixing one cable end of the brake to a point set at a certain

height and joining the other end to a block, which is

allowed to fall freely (Fig. 8b). By choosing the fall height

and block weight, the energy that the brake absorbs can be

controlled. Load during all the test is registered by a load

cell. The load–time curve is obtained (Table 2). The dis-

placement is only measured at the end, meaning a constant

velocity assumption during the whole test, and the inter-

mediate displacements are assumed to be proportional to

time. This assumption is not totally adequate, especially in

friction processes, where fluctuations are caused by alter-

nating slippage and stop. In this arrangement, results from

quasi-static (force vs displacement) and dynamic tests

(force vs time) performed on the same brakes by these

authors cannot be directly compared. The analysis of both

tests can be only be done by observing the differences in

the performance of the brake and the force level of the

brake throughout the test.

3.2.3 Dynamic Test (Type 2)

This dynamic test system (Tajima et Al. 2009; Tran et al.

2013a) consists of a brake connected to a horizontal cable

anchored at both ends. A weight drops vertically and

impacts on the cable (Fig. 8c). This event makes the brake

work, and the load is measured with a load cell. Simulta-

neously, the increase in length of the cable is observed on a

vertical measurement scale. The basic disadvantage of this

laboratory test is its complexity. A big structure is needed

to hold the weight before the free falling, and a runway also

needs to be installed in order to attach the cable in its

Table 2 Behaviour curves of different brakes extracted from dynamic tests

DYNAMIC TEST 1: FREE FALLING BLOCK

(Trad et al., 2013; Bertrand et al., 2012)

DYNAMIC TEST 2: IMPACT(Tran et al, 2013a)

DYNAMIC TEST 3: FULL BARRIER(Fulde et al., 2013)

=45 kN=22 kN=-=-/ =-

=133.2 kN= 60 kN=54.1 mm=630 mm/ =58.52 kJ/m

=65 kN=93 kN=-=-/ =-

=125 kN=150 kN=125 mm=1750 mm/ =130.71 kJ/m

=56 kN= 50.2 kN=16.5 mm=770 mm/ =46.53

kJ/m

I

II

III

IV

V

The first column shows the results from the vertical dynamic test. The data of the second column are extracted from the dynamic test where the

set brake ? cable is horizontally fixed and the weight impact is in the vertical direction. The third column corresponds to full-scale barrier tests

L. Castanon-Jano et al.

123

position. Curves obtained from dynamic test type 2 are

given in Table 2.

3.2.4 Dynamic Test (Type 3)

Another way to study the dynamic behaviour of energy

dissipaters is carrying out an impact test on a full barrier,

registering the force measurement of each brake and

observing its performance (Fulde and Müller 2013)

(Table 2). In order to avoid the interaction of the results,

only one brake per cable is recommended. The advantage

of this type of tests is that the study of the brake behaviour

is at the same speed as under real conditions. The disad-

vantage is the need for a big infrastructure to perform the

tests.

3.2.5 Behaviour Analysis from Experimental Test Data

Concerning the results from static tests, it can be seen that

curves from brakes 1, 2, 4 and 9 in Table 1 do not show a

hardening section BC, because the test has been stopped

before reaching this situation, bearing in mind that under

real conditions the brake should not reach high force values

close to the ultimate strength of the cable.

Section AB has different paths depending on the type of

brake. The oscillations in friction brakes (cases 1, 2, 3, 4)

are due to the sequential slippage and stopping of the

cables in the clamps. The different curves for the same

brake correspond to different bolt torques. Force softening

in brakes 1 and 4 could be related to the abrasion of the

surfaces in contact. Moreover, brake 8 seems to have some

waves, due to asymmetric displacement of the U arms

through the compression sleeves. Fluctuations in brake 6

are a consequence of the plastic deformation due to local

buckling of the square profile (Trad. 2011). The sawtooth

curve of brake 9 is generated by the sequential plastic

deformation until failure of the material between the holes

(Fulde and Müller 2013).

The elastic section OA is missing in one curve of brake

8 (corresponding to the brake with a sleeve pressure of

140 bar). This is due to the initial load applied on the brake

before the beginning of the static test to help the brake to

accommodate to the machine clamps. The measurement of

displacements begins after this accommodation, so the

curve displayed has a nonzero initial load.

Force and displacement data at the activation and stiff-

ening points are shown in Tables 1 and 2, as well as the

ratio between absorbed energy and maximal displacement.

The absorbed energy is calculated by integrating the area

under the force–displacement curve and removing the

elastic component at the end of the test:

Eabs=d ¼r dmax0 F � dd�

F2C�dA

2FA

dmaxð1Þ

As can be seen in brakes 1, 4 and 8, the bolt torque or the

sleeve pressure affects the ratio Eabs=d to a great extent.A quantitative analysis of the brakes is not possible due

to the differences in the nature of the load applied in the

tests (static or dynamic), the characteristics of the cables in

which they are inserted and the geometric differences

among the brakes. Hence, a qualitative analysis will be

performed and normalized graphs are presented to show

the different responses in brakes with the same energy

dissipation mechanisms (Figs. 10, 11).

Activation forces (FA) of the brakes in Table 1 are

analysed in Fig. 10 in a non-dimensional way. FA can vary

in a similar brake type as occurs in most of the friction

brakes, where bolt torque is a parameter that can change

the pressure between the surfaces in contact and, hence, the

whole behaviour curve. In order to avoid a risk situation,

the activation force should not be close to the breaking load

Fig. 10 Non-dimensionalanalysis of activation point A in

Table 1 in terms of the ratio of

activation force to final force

and the ratio of activation

displacement to total

displacement

Energy Dissipating Devices in Falling Rock Protection Barriers

123

of the cable, especially in brakes where friction is incor-

porated in the dissipation method (friction and mixed). If

the activation force of a brake is close to the breaking load

of the cable and pressure in friction brakes is not applied

accurately, the brake will suffer an elastic behaviour

response until the rupture of the cable, and it would not

accomplish its dissipation goal.

The effect of the decrease in the force after the activa-

tion of the brakes 1 (B1) and 4 (B4) is observed in Fig. 10,

the activation force being the maximum of the curve and

the final force being between 20 and 90 % less than FA.

Mixed brakes have the lowest quotient FA/Ffinal, and the

partial failure brake B9 has a quotient Fa/Ffinal equal to one

as the mean force of the A-B section is horizontal.

Differences in the maximum force tolerated in Table 1

may be due to the characteristics of the cables: diameter,

configuration of the strands, number of strands and type of

steel.

Continuing the dimensionless analysis, two parameters

E* and d * are proposed. E* is defined as the ratio of the

energy of the brake and the maximum value of the brake’s

energy at the end of the test, and d* is the ratio of theelongation of the brake and its maximum value of

elongation:

E� ¼r d0 F � ddr dmax0 F � dd

ð2Þ

d� ¼ ddmax

ð3Þ

These two parameters are related to Fig. 11.

In all the curves in Fig. 11, there is an initial quasi-

horizontal section, corresponding to the initial behaviour of

the brakes with a low increment in deformation and high

increment in load that demonstrates low elastic energy and

hence a low increment in E*. After this small section,

sometimes invisible due to their low displacement per-

centage of the total, absorbed (non-recoverable) energy

appears with a higher slope. A straight slope means a

constant increment in energy during the working of the

Fig. 11 E* versus d� grouped by their dissipation method: a friction brakes (from 1 to 4), b mixed brakes (from 5 to 8) and c partial failure brake(9)

L. Castanon-Jano et al.

123

brake, as can be seen in brake 3 until d� = 0.9, in brakes 4with a torque of 9 daNm and in brake 9. Other brakes show

two successive decreasing slopes, meaning a first part with

a higher increment in the proportion of energy absorbed

than the next as happens in brakes type 1 and in brake 4

with 18 daNm of torque. Finally, two successive increasing

slopes mean that at the end of the brake working, it has a

higher increment in absorbed energy than at the beginning.

This happens in all the mixed brakes, this behaviour being

more pronounced in brake 8 with a pressure of 120 bar.

The performance of dynamic tests has a great relevance

in order to evaluate the differences in the behaviour of a

brake due to inertia and load speed. These two dynamic

variables were not considered by Peila et al. (1998); as a

result, an unexpected behaviour was obtained, reflected in

the non-activation of some of the brakes in the barrier tests.

At this juncture, Trad et al. (2013) performed both types

of tests on a friction brake (Fig. 3d) and on a mixed friction

deformation brake (Fig. 6d) (first column in Table 2).

Although displacement was not measured in the dynamic

test, a comparison among forces in both processes was

made, with totally different results. Activation force in the

pure friction brake reduced 50%, and from that point, force

did not remain constant, as happened in the static case, but

decreased. Dynamic test type 2 performed on friction

brakes (second column in Table 2) also shows a reduction

in the amplitude of the peaks at the end. However, in the

deformation brake (no 6 in Table 1 and II in Table 2),

activation force and mean force in the operational section

were similar in both tests.

The differences in the friction brakes may be due to the

wear of the pressure pieces or the dilatation of the material

due to the rising temperature in the friction area. It can be

concluded that friction brakes are highly sensitive to speed

variation. This is coherent with the results of Peila et al.

(1998) who used friction brakes in his study. It cannot be

stated that tests on other brakes with a different dissipation

mechanism will not be affected by dynamic variables, so a

dynamic test must be performed in any case. In brakes

working by deformation of any of their components

(Sects. 2.2 and 2.3), the strain rate effect affects the stress

values so the materials mechanical properties could vary

with the process dynamics and the force–deformation

curves could also be sensitive to the test speed. The logical

next step is to find out whether changes in the speed of the

dynamic tests, maintaining the same absorbed energy, can

also make the brakes behaviour vary. If this hypothesis is

verified, dynamic tests should be done at the same speed as

in the barrier.

The measurement of the elongation in the brake must

also be registered in the dynamic test. The supposition

made by Trad et al. (2013), where a linear relationship

between displacement and time is assumed, was discarded

by Tajima et al. (2009), who demonstrated that in the last

instant of the test the elongation-time curve flattens; that is,

the speed is not constant.

3.3 Numerical Simulations

Concerning the research and development of brakes, finite

element method (FEM) software is commonly used to help

engineers to design and optimize their geometry, as well as

to find out what the suitable places in the barrier are to

locate brakes. During the energy dissipation of a brake,

there are several phenomena which affect the set-up of the

simulations: the brakes suffer large displacements, as

shown from the curves in Table 1; abrupt-changing inter-

actions in friction brakes as a consequence of the sliding

process; and plasticity of materials as a dissipation method

in deformation and mixed brakes. These three nonlineari-

ties can be confronted using both implicit and explicit

algorithms. However, explicit analysis is preferred due to

the reduction in the computational cost in high-speed

dynamic problems (Sun et al. 2000).

Two ways of dealing with the simulation of brakes can be

established, depending on the objective of the simulation.

The first concerns the improvement of the geometrical

design, optimization of shape and dimensions and the

analysis of the dissipation mechanisms within the brake.

Three-dimensional models are created for this purpose,

introducing realistic geometries, material characterization

for each part of the brake and ‘contacts between them.

These models are focused on the brake, avoiding the place

in which they are located and applying loads and boundary

conditions directly on both brake ends. The optimization of

the design has to be preceded by a calibration of a refer-

ence model, from which a parametric study can be done,

searching for the maximum absorbed energy. Since each of

the parts in the brake is modelled in detail, weak points can

be detected and modified in the prototype. The simulations

carried out by Castro-Fresno et al. (2009) and del Coz et al.

(2010) in Ansys software helped to verify the correct

performance of the brakes (B8), obtaining energy absorp-

tion values very similar to the results of the experimental

tests. Several solutions to improve the brake geometry

arose, and efficient sleeve pressure was established. Like-

wise, Trad et al. (2013) performed, in CAST3 M software,

a study of the optimal thickness, length and material of a

square profile, employed as the main part of a brake design.

The second way of dealing with a simulation takes into

account the behaviour at the scale of the complete struc-

ture, achieving a cost-effective method for the study of the

barrier optimization. When a flexible barrier is simulated in

FE software, the large amount of elements and the

Energy Dissipating Devices in Falling Rock Protection Barriers

123

nonlinearities such as plasticity of materials or interactions

require large computational cost to solve the problem.

Thus, a simpler one-dimensional model of the brake should

be implemented. The properties of the simplified brake

vary depending on the software and author, and they are

summarized in Table 3. Axial connectors and truss ele-

ments are effectively used for modelling the brake. Few

differences exist between these two approaches. In an axial

connector, the relative displacement is measured along the

connector axis, and the local coordinate system rotates as

the nodes change position. Truss elements transmit force

axially only and are 3-DOF elements, which allow trans-

lation only and do not permit rotation and resistance to

bending.

Themain differences are the following: cross-sectional area

is required for trusses, and their behaviour is defined by a

stress–strain law; on the contrary, axial connectors are not

meshable and they are controlled by a force–displacement law.

The cases compiled in Table 3 use one of the four

experimental procedures explained in Sect. 3.2 (quasi-sta-

tic test, dynamic test 1, dynamic test 2 or full-scale test).

Usually, when incorporating the 1D element in the full

barrier model, it simply consists of interrupting the lateral

or upstream cables and placing the truss or the axial con-

nector with a three-linear or four-linear behaviour law

(Fig. 12a). However, Dhakal et al. (2011) and Tran et al.

(2013a, b) changed this configuration, adding ‘‘protection

cables’’ (Fig. 12b). When the stroke of the brake ends, the

protection cables, with their corresponding stiffness, begin

to work as if a new branch of the graph were defined.

Both configurations are correct and should have similar

results. However, a single 1D element configuration

(Fig. 12a) is preferred because of the smaller number of

elements, saving computational time.

A hybrid case between the two ways of dealing with a

brake simulation is presented by Gentilini et al. (2013),

who employed Abaqus to model a 3D brake in static and

dynamic conditions, not searching for the optimal design,

but looking for the parameters for their use in a 1D model

to be included in a full-scale barrier test.

Special mention is required for software based on dis-

crete element method (DEM). DEM programs are based on

the motion and interaction of a large number of small

particles. Like FEM, DEM has the capacity to solve

implicit and explicit algorithms and confront nonlineari-

ties. Initially, this method was focused on the modelling of

granular materials, but nowadays it can be applied in other

applications, sometimes combined with FEM. Limitations

in computational time are similar for both methods: the

number of degrees of freedom for FEM and number of

particles for DEM.

Nicot et al. (2001) and Bertrand et al. (2012) performed

their full-scale simulations by means of DEM models.

However, only the latter details the data entered for the

definition of the brake. Parameters were extracted from

tensile tests under dynamic conditions, and four different

approaches were taken depending on the technology of the

brake (friction/buckling, elastic perfectly plastic or brittle

damageable). Calculations were completed successfully,

and the three brakes were compared in the context of the

full barrier.

4 Conclusions

This paper has offered a classification based on the method

used to transform and/or dissipate the energy induced by a

rockfall on a cable net. A qualitative analysis was carried

out of the behaviour curves from static and dynamic tests.

Three different kinds of behaviour were identified: the first

has a linear increment in the proportion of absorbed energy

during its working, the second has an initial higher incre-

ment in the percentage of absorbed energy than in the final

part; and, the last one, whose percentage of dissipated

energy is higher in the final part of the working of the

brake. A linear or sequential increasing slope of E* is

preferred, since a lower slope of E* in the final part of the

graph means a loss of resistance of the brake.

The amplitude of the peaks in the force–displacement

curves due to the slippage and stopping in friction brakes or

to local buckling in deformation brakes can be larger with a

dynamic behaviour than with the static analysis. Moreover,

peak forces can be more than 100% higher than the acti-

vation force. In order to prevent a rupture caused by an

unexpected high load peak, an activation force less than

50% of the rupture force of the cable is recommended for

future design processes of brakes.

Further analysis of the variability of friction brakes

under wet conditions, like rain or dew, is suggested. Water,

acting as a lubricant liquid, may affect the friction coeffi-

cient. If this factor has a great influence in the energy

dissipation capacity, friction brakes would not be adequate

to install in flexible barriers located in rainy or humid

places.

Due to differences between low-speed and high-speed

tests regarding activation force and mean operation force,

the execution of dynamic tests, more similar to the real

conditions of the brake, is preferable over static tests. Trad

(2011) performed a large amount of tests with different

speeds, materials and energies. However, these three

parameters were not studied independently so no conclu-

sions were obtained regarding this topic. The correct

analysis should be based on the execution of at least 9 tests

at 3 different speeds (3 tests for each speed in order to

obtain representative values) maintaining the same absor-

bed energy, that is, regulating the height of the falling

L. Castanon-Jano et al.

123

Table 3 Brake models in numerical simulations of full-scale barriers

References 1D model type Behaviour law Parameters from

ABAQUS

Cazzani

et al.

(2002)

Truss elements

Displacement

Forc

e

Quasi-static tensile test on the brake

Gentilini

et al.

(2012)

Tension only truss

Forc

e

Displacement

Data recorded by the load cells located at the two outermost uphill

anchorages in the MEL and SEL experiments on the tested barriers

(dynamic conditions)

Gentilini

et al.

(2013)

Axial connector

Forc

e

Displacement

3D model used to obtain the F-d graph and adjust 1D modelparameters. Static and dynamic conditions

Escallon

et al.

(2014)

Axial connector

Displacement

Forc

e

Quasi-static tensile test on the brake

LS-DYNA

Dhakal

et al.

(2011)

Discrete truss element

for the brake.

Protection cables added

as discrete truss

elements. Displacement

Forc

e

Dynamic falling-weight impact test

Dhakal

et al.

(2012)

Discrete truss element

Displacement

Forc

e

Cazzani brake model (quasi-static tests)

Displacement

Forc

e

Dynamic falling-weight impact test

Tran et al.

(2013b)

Discrete truss element

for the brake.

Protection cables added

as discrete truss

elements. Displacement

Forc

e

Dynamic falling-weight impact test

Moon

et al.

(2014)

Discrete beam

Displacement

Forc

e

Peila et al. (1998) and Cazzani et al. (2002) brake model (quasi-static

tests)

FARO

Grassl

et al.

(2003)

Tension only truss

Displacement

Forc

e

Quasi-static tensile test

Energy Dissipating Devices in Falling Rock Protection Barriers

123

weight. With the aim of clearly observing the differences in

the curves (if they exist), the speed values for the tests

should be spaced at a minimum of 5 m/s, choosing, for

example, v1 = 10 m/s, v2 = 15 m/s and v3 = 20 m/s. The

dynamic test configuration can also be improved. The free

falling block test does not record displacement measure-

ment over time. The impact test does so; however, the test

frame is large and not cost-effective. A new design of tests

mixing the simplicity of the free falling block test and the

accuracy of the impact test should be developed for the

future.

The choice of number and arrangement of the devices in

the barrier is an essential aspect to appropriately work and

will depend, to a great extent, on the total absorbed energy.

In spite of the importance of this point, there is no stan-

dardized methodology that defines either the location or the

energy level that each brake must absorb to achieve an

optimum performance. Measurement of force and dis-

placement in each brake of the full barrier test is recom-

mended for future analysis, observing whether the brakes

behave in the same way as was determined by static and

dynamic ‘‘only-brake’’ tests and obtaining the energy level

reached and the percentage of energy dissipated. This

information was not obtained in any full-scale test, and it is

considered essential for design optimization. Force mea-

surement can be taken with cable sensors, like those used

by Blanco-Fernandez et al. (2013), which are able to take

the data without cutting the cable.

Several finite element and discrete element software

packages are employed as a support tool in the design

process. Three-dimensional models help geometry opti-

mization, and one-dimensional brake models are imple-

mented in the analysis of the full barrier with the aim of

verifying the suitability of the position and energy

capacity of brakes. The behaviour law in 1D models is

obtained with static tests in most cases. The reason could

be the information provided in the last (and stiffer) part

of the curve, which is not obtained with dynamic tests.

The main suggestion in this aspect is the correction of

activation force and mean force if they are different

from the static ones.

Acknowledgements The authors would like to acknowledge Incha-lam Bekaert for financial support and Malla Talud Cantabria for the

information provided.

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Energy Dissipating Devices in Falling Rock Protection BarriersAbstractIntroductionDescription of the Existing BrakesBrake Elements by Pure FrictionBrake Elements by Plastic DeformationBrake Elements by Partial FailureMixed Brake Elements: Friction/Deformation

DesignDesign CriteriaExperimental TestsQuasi-Static TestDynamic Test (Type 1)Dynamic Test (Type 2)Dynamic Test (Type 3)Behaviour Analysis from Experimental Test Data

Numerical Simulations

ConclusionsAcknowledgementsReferences

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